Surface gravitational field and topography changes induced by the Earth’s fluid core motions

Abstract.

Using a Love number formalism, the elastic deformations of the mantle and the mass redistribution gravitational potential within the Earth induced by the fluid pressure acting at the core–mantle boundary (CMB) are computed. This pressure field changes at a decadal time scale and may be estimated from observations of the surface magnetic field and its secular variation. First, using a spherical harmonic expansion, the poloidal and toroidal part of the fluid velocity field at the CMB for the last 40 years is computed, under the hypothesis of tangential geostrophy. Then the associated geostrophic pressure, whose order of magnitude is about 1000 Pa, is computed. The surface topography induced by this pressure field is computed using Love numbers, and is a few millimetres. The mass redistribution gravitational potential induced by these deformations and, in particular, the zonal components of the related surface gravitational potential perturbation (ΔJ₂, ΔJ₃ and ΔJ₄ coefficients), are calculated. Overall perturbations for the J₂ coefficient of about 10⁻¹⁰, for J₃ of about 10⁻¹¹ and for J₄ are found of about 0.3×10⁻¹¹. Finally, these theoretical results are compared with recent observations of the decadal variation of J₂ from satellite laser ranging. Results concerning ΔJ₂ can be described as follows: first, they are one order of magnitude too small to explain the observed decadal variation of J₂ and, second, they show a significant linear trend over the last 40 years, whose rate of decrease amounts to 7% of the observed value.